NEWS
- Title
- Plastic tensor networks for interpretable generative modeling
- Author
- Katsuya O. Akamatsu, Kenji Harada, Tsuyoshi Okubo, Naoki Kawashima
- Abstract
- A structural optimization scheme for a single-layer nonnegative adaptive tensor tree (NATT) that models a target probability distribution is proposed as an alternative paradigm for generative modeling. The NATT scheme, by construction, automatically searches for a tree structure that best fits a given discrete dataset whose features serve as inputs, and has the advantage that it is interpretable as a probabilistic graphical model. We consider the NATT scheme and a recently proposed Born machine ATT optimization scheme and demonstrate their effectiveness on a variety of generative modeling tasks where the objective is to infer the hidden structure of a provided dataset. Our results show that in terms of minimizing the negative log-likelihood, the single-layer scheme has model performance comparable to the Born machine scheme, though not better. The tasks include deducing the structure of binary bitwise operations, learning the internal structure of random Bayesian networks given only visible sites, and a real-world example related to hierarchical clustering where a cladogram is constructed from mitochondrial DNA sequences. In doing so, we also show the importance of the choice of network topology and the versatility of a least-mutual information criterion in selecting a candidate structure for a tensor tree, as well as discuss aspects of these tensor tree generative models including their information content and interpretability.
- Comments
- 21 pages, 17 figures
- Citation
- Katsuya O. Akamatsu, Kenji Harada, Tsuyoshi Okubo, and Naoki Kawashima, Machine Learning: Science and Technology 7 015014(2026)
- DOI
- 10.1088/2632-2153/ae3048
- Code
- Nonnegative Adaptive Tensor Tree Modeling
- Date
- December 15, 2025
- Conference
- Mini-workshop: Tensor Network algorithms and applications 2025 (Tainan, National Cheng Kung University, Taiwan)
- Title
- Structure-Optimized Tensor Network Generative Models for Data Distributions
- Title
- Improving the accuracy of the tree-tensor network approach by optimization of network structure
- Author
- Toshiya Hikihara, Hiroshi Ueda, Kouichi Okunishi, Kenji Harada, and Tomotoshi Nishino
- Abstract
- Numerical methods based on tensor networks have been extensively explored in the research of quantum many-body systems in recent years. It has been recognized that the ability of tensor networks to describe a quantum many-body state crucially depends on the spatial structure of the network. In the previous work [T. Hikihara et al., Phys. Rev. Res. 5, 013031 (2023)], we proposed an algorithm based on tree-tensor networks (TTNs) that automatically optimizes the structure of a TTN according to the spatial profile of entanglement in the state of interest. In this paper, we apply the algorithm to the random 𝑋𝑌 -exchange model under random magnetic fields and the Richardson model in order to analyze how the performance of the algorithm depends on the detailed updating schemes of the structural optimization. We then find that for the random 𝑋𝑌 model, on the one hand, the algorithm achieves improved accuracy, and the stochastic algorithm, which selects the local network structure probabilistically, is notably effective. For the Richardson model, on the other hand, the resulting numerical accuracy subtly depends on the initial TTN and the updating schemes. In particular, the algorithm without the stochastic updating scheme certainly improves the accuracy, while the one with the stochastic updates results in poor accuracy due to the effect of randomizing the network structure at the early stage of the calculation. These results indicate that the algorithm successfully improves the accuracy of the numerical calculations for quantum many-body states, while it is essential to appropriately choose the updating scheme as well as the initial TTN structure, depending on the systems treated.
- Comments
- 19 pages, 17 figures, 2 tables
- Citation
- Toshiya Hikihara, Hiroshi Ueda, Kouichi Okunishi, Kenji Harada, Tomotoshi Nishino, ``Improving the accuracy of the tree-tensor network approach by optimization of network structure'', Phys. Rev. B 112, 134427 (2025)
- DOI
- 10.1103/ljj8-tkpc
- Code
- Demo code
- Dates
- August 25-29, 2025
- Conference
- SQAI-NCTS Workshop on Quantum Technologies and Machine Learning (National Taiwan University, Taipei, Taiwan)
- Title
- Adaptive Tensor Tree Method with Annealing of Mini-batch Samples for Generative Modeling on Quantum Devices
- Abstract
- We proposed the Adaptive Tensor Tree (ATT) method, which uses the tensor tree network within the Born machine framework to construct a generative model. This method expresses the target distribution function as the squared amplitude of a quantum wave function represented by a tensor tree. The core concept of the ATT method involves dynamically optimizing the tree structure to minimize the bond mutual information. In this presentation, we introduce a new technique that utilizes an annealing process on mini-batch samples to enhance the performance of the ATT method. We will demonstrate the effectiveness of this new ATT approach using various datasets.
- Title
- Tensor tree learns hidden relational structures in data to construct generative models
- Author
- Kenji Harada, Tsuyoshi Okubo, Naoki Kawashima
- Abstract
- Based on the tensor tree network with the Born machine framework, we propose a general method for constructing a generative model by expressing the target distribution function as the amplitude of the quantum wave function represented by a tensor tree. The key idea is dynamically optimizing the tree structure that minimizes the bond mutual information. The proposed method offers enhanced performance and uncovers hidden relational structures in the target data. We illustrate potential practical applications with four examples: (i) random patterns, (ii) QMNIST handwritten digits, (iii) Bayesian networks, and (iv) the pattern of stock price fluctuation pattern in S\&P500. In (i) and (ii), the strongly correlated variables were concentrated near the center of the network; in (iii), the causality pattern was identified; and in (iv), a structure corresponding to the eleven sectors emerged.
- Comments
- 10 pages, 3 figures
- Citation
- Kenji Harada, Tsuyoshi Okubo, and Naoki Kawashima, Machine Learning: Science and Technology 6 025002(2025)
- DOI
- 10.1088/2632-2153/adc2c7
- Code
- Adaptive Tensor Tree Generative Modeling
- Date
- December 13th, 2024
- Seminar
- Theory seminar at ISSP, Univ. of Tokyo
- Title
- Tensor tree learns hidden relational structure in data to construct generative models
- Abstract
-
Generative modeling is a significant machine learning technique that constructs the probability distribution of a dataset, owing to its wide range of applications across various problems. Recently, there has been extensive research into generative modeling on quantum computers, referred to as Born machines. This approach utilizes the output of projective measurement of quantum states for stochastic samplings.
We propose a general method for constructing a generative model based on the tree tensor network within the Born machine framework. The core idea is to optimize the tree structure dynamically to minimize the bond mutual information. We demonstrate potential applications with four examples: (1) Random bit sequences with long-range correlation, (2) Images of handwritten digits from the QMNIST dataset, (3) Bayesian networks, (4) Stock price fluctuations in the S&P 500.
Our method significantly enhances performance and reveals hidden relational structures in the target data, paving the way for future improvements and advancements.
- Reference
- arXiv:2408.10669
- Code
- Adaptive Tensor Tree Generative Modeling
TOPICS
Toolkit of Bayesian Scaling Analysis
Reference application software of a new scaling analysis method of critical phenomena based on Bayesian inference.
To demo To detailsToolkit of Adaptive Tensor Tree Generative Modeling
Reference application software of adaptive tensor tree generative modeling.
To GitHubMonte Carlo simulations
This demonstration shows a Monte Carlo simulation of the two-dimensional Ising model by three algorithms: Metropolis, Swendsen-Wang, and Wolff algorithms.
To demoABOUT
Kenji Harada
(
原田健自
)
Assistant Professor,
Graduate School of Informatics, Kyoto University, Japan.
harada.kenji.8e@kyoto-u.ac.jp
Room 203, Research Bldg. No.8, Yoshida Campus, Kyoto Univ., Kyoto, 606-8501, Japan.
Map (No.59)
orcid.org/0000-0003-0231-7880